Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
r, c = map(int, input().split(' '))
arr = []
ops = []
num_ops = 0
for i in range(r):
  arr.append(list(map(int, input().split(' '))))

s1, s2 = "row ", "col "
if r > c:
  arr1 = []
  for i in range(c):
    arr1.append([0]*r)
  for i in range(r):
    for j in range(c):
      arr1[j][i] = arr[i][j]
  r, c = c, r
  s1, s2 = s2, s1
  arr = arr1

for i in range(r):
  m = min(arr[i])
  if m > 0:
    arr[i] = [x -m for x in arr[i]]
    ops.append((0, i, m))
    num_ops += m

possible = True
for i in range(c):
  a = arr[0][i]
  for j in range(1, r):
    if arr[j][i] != a:
      possible = False
      break

  if possible == False:
    break

  if a > 0:
    ops.append((1, i, a))
    num_ops += a


if possible:
  print(num_ops)
  for i in ops:
    if i[0] == 0:
      for k in range(i[2]):
        print(s1 + str(i[1]+1))
    else:
      for k in range(i[2]):
        print(s2 + str(i[1]+1))
else:
  print(-1)